All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
It is impermissible for a woman to go out while wearing perfume if she will pass by men who will detect her good smell. If a woman does this, then she is sinful and described by a Hadeeth as an adulteress. However, it does not imply the real meaning of adultery, which causes one to incur the corporal punishment. Rather, it is the adultery of the eyes, which takes place when men look at her (that is intended here). Explaining the Hadeeth, Al-Munawi commented, "She has aroused men's desires with her smell and made them look at her. In fact, whoever looks at her has committed adultery with his eye because of her and, therefore, she is deemed guilty by the Sharee’ah."
If a woman applies perfume and then wants to go out to the Masjid or any other place, she has to wash herself by making Ghusl, not because she is in a state of janabah, but in order to remove the trace of perfume. It was narrated on the authority of Abu Hurayrah that the Messenger of Allah, sallallaahu ‘alayhi wa sallam, said, "If a woman goes out to the Masjid, then she has to make Ghusl similar to that for janabah in order to remove the smell of perfume in the same way that she makes Ghusl to remove the janabah." [An-Nasa’i]
Commenting on the Hadeeth, Al-Qari said:
She has to make Ghusl similar to that of janabah by washing her whole body with water, if she perfumed her whole body, so that the smell of perfume is removed. If she only perfumed a specific spot of her body, however, then she has to wash this spot in specific. If she perfumed her clothes, then she has to either change them or remove the smell of perfume from the clothes. She is required to do this only if she wants to go out of her home. As long as she is at home, she is not required to do so.
Allah knows best.